Logarithm. Examples: log_2 8 - logarithm of 8 with base 2. log_4 16 - logarithm of 16 with base 4. log 1000 - common logarithm of 1000 (base equal 10). ln 7 - natural logarithm of 7 (base equal e ≈ 2.718). The logarithm of b with base a: log_a b. Conditions for the base a: a * 0 i a ≠ 1. Conditions for the number b: b * 0. The definition of a logarithm: log_a b = x if a^x = b. Examples: log_2 8 = 3 - because 2^3 = 8. log_4 16 = 2 - because 4^2 = 16. log 1000 = 3 - because 10^3 = 1000.